RL Circuits
An RL circuit. When the the When to no The it is uld
Energy in a Magnetic Field
Iε as the rate at which energy is supplied by the battery and I2R as the rate at which energy is delivered to the resistor 
Energy in a Magnetic Field
We can also determine the energy density of a magnetic field. 
Еhe magnetic energy density, or the energy stored per unit volume in the magnetic field of the inductor is
Mutual Inductance
A cross-sectional view of two adjacent coils. A current in coil 1 sets up a magnetic field and some of the magnetic field lines pass through coil 2.
Еhe mutual inductance M12 of coil 2 with respect to coil 1:
Mutual inductance depends on the geometry of both circuits and on their orientation with respect to each other.
Mutual Inductance
The emf induced by coil 1 in coil 2 is
If the current I2 varies with time, the emf induced by coil 2 in coil 1 is
In mutual induction, the emf induced in one coil is always proportional to the rate at which the current in the other coil is changing.
Oscillations in an LC Circuit
A simple LC circuit. The capacitor has an initial
charge Qmax, and the switch is open for t > 0 and then
closed at t = 0.
Oscillations in an LC Circuit
Oscillations in an LC Circuit
Mutual Inductance
The natural frequency of oscillation of the LC circuit.